Question

What is the value of the expression

172,000
338,650
515,100
1,015,050

Answer 1

`\displaystyle\sum_(i=1)^z~i^2\implies \cfrac{z(z+1)(2z+1)}{6} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\sum_(n=1)^(100)~(3+n^2)\implies \begin{array}{llll} \displaystyle \sum_(n=1)^(100)~3~~ &+& ~~\displaystyle \sum_(n=1)^(100)~n^2\\\\\\ (100)(3)&+&\cfrac{100(100+1)( ~~ 2(100)+1 ~~ )}{6} \\\\\\ 300&+&\cfrac{100(101)(201)}{6} \\\\\\ 300&+&338350 \\\\\\ &&\textit{\LARGE 338650} \end{array}`

Answer 2

The correct answer is 338,650